Microscopic Disorder-Based model for non-Abelian Quasi-Particles in $\nu=5/2$ FQH states*

The detection of non-Abelian quasiparticles remains an outstanding experimental problem in the $\nu=\frac{5}{2}$ fractional quantum Hall (FQH) state. The presence of non-Abelian statistics would lead to additonal low energy states in the system, and hence an additional low-temperature entropy. One approach to test for non-Abelian quasiparticle statistics uses thermodynamic measurements to detect this entropy contribution~[1,2]. We present a microscopic model for quasiparticles in the $\nu=\frac{5}{2}$ FQH state with a disorder potential that fluctuates on the order of several magnetic lengths, and attempt to determine the feasibility of the experiments proposed in~[1], based on local probe measurements of incompressibility~[3]. \\ \ [1] Cooper, N.R., Stern, A. PRL. {\bf 102}, 176807 (2009). \\ \ [2] Yang, K., Halperin, B.I. PRB {\bf 79}, 115317 (2009). \\ \ [3] Venkatachalam, V., Yacoby, A., Pfeiffer, L., West, K. Nature {\bf 469}, 185 (2011).